What's That Famous Wizard Doing in My Homework?

Here we see an assignment for Complex Variables II. The picture may be a little hard to see. I didn't have a scanner to scan it. Instead I took a picture with my high quality camera phone. Maybe a better picture will make its way up here eventually.

What the question asks is:
Show how to define [(1+z)/(1-z)]^1/2 as a single-valued analytic function f(z) in the z-plane slit along the real segment [-1,1], with f(z) defined to be +1 at z=0 on the upper edge of the slit. What is the relation between the values of f(z) on the upper and lower edges of the slit?

Here is an overview of my answer:


First, I converted this into an exponential equation:
[(1+z)/(1-z)]^1/2 = e^[1/2 log(1+z)+1/2 log(1-z)]
I illustrated this in the graph to the left.
Then: "Poof! Proof by magic!"


In the enlarged picture, you can see Harry Potter with his lightning scar. I added the wand with an arrow pointing to it to let the grader know that "There's a phoenix feather in there!" Some people aren't aware of these things.

You might think that I forgot to answer the crucial part of the question. NOPE! It's in there too! "They're related by half-blood princes!"


Clearly, the grader was impressed. I got a "Nice." He took off half though. I think it was because of my grammar... related by half-blood princes? What was I thinking?